Related papers: A Solution to Galileo's Enigma "Mostro Son Io"
The 6th problem of the 50th International Mathematical Olympiad (IMO), held in Germany, 2009, is called 'the grasshopper problem'. To this problem Kos developed theory from unique viewpoints by reference of Noga Alon's combinatorial…
Maybe the first inverse problem presented in the history of the occidental thought is described in the book Republic, written by Plato. The problem is posed in the Book VII in a text known as the Allegory of the Cave. That text motivated us…
The case of the Zodiac Killer is one of the most widely known unsolved serial killer cases in history. The unidentified killer murdered five known victims and terrorized the state of California. He also communicated extensively with the…
Nine years ago,working within the framework of theoretical dense matter physics,the present author has determined the chemical composition of the Galileian satellites of Jupiter.A few months ago,in the flyby of the GA- LILEO spaceprobe,some…
This article introduces a pedagogical method for {\it solving combinatorial problems} that frequently involve structures that are unfamiliar or less familiar. Indeed, an indirect method has been proposed in order to evade any possible…
The modified measure theories recommend themselves as a good possibility to go beyond the standard formulation to solve yet unsolved problems. The Galileon measure that is constructed in the way to be invariant under the Galileon shift…
Some verses of Dante Alighieri suggest his astrological sign and his probable date of birth. This leads us to reflect on the different methods, increasingly divergent, with which sciences as opposed to beliefs approach reality.
Vortex solutions are topologically stable field configurations that can play an important role in condensed matter, field theory, and cosmology. We investigate vortex configuration in a 2+1 dimensional Abelian Higgs theory supplemented by…
We present a natural, combinatorial problem whose solution is given by the meta-Fibonacci recurrence relation $a(n) = \sum_{i=1}^p a(n-i+1 - a(n-i))$, where $p$ is prime. This combinatorial problem is less general than those given in [3]…
Meyniel's conjecture is one of the deepest open problems on the cop number of a graph. It states that for a connected graph $G$ of order $n,$ $c(G) = O(\sqrt{n}).$ While largely ignored for over 20 years, the conjecture is receiving…
We approach several themes of classical geometry of the circle and complete them with some original results, showing that not everything in traditional math is revealed, and that it still has an open character. The topics were chosen…
We review Fermi's paradox (or the "Great Silence" problem), not only arguably the oldest and crucial problem for the Search for ExtraTerrestrial Intelligence (SETI), but also a conundrum of profound scientific, philosophical and cultural…
Galileons are higher-derivative theories of a real scalar which nevertheless admit second order equations of motion. They have interesting applications as dark energy models and in early universe cosmology, and have been conjectured to…
The Giornata Sesta about the Force of Percussion is a relatively less known Chapter from the Galileo's masterpiece "Discourse about Two New Sciences". It was first published lately (1718), long after the first edition of the Two New…
The classical platonist / formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: \emph{Is new mathematics discovered or invented? Using examples from my own mathematical work during the…
Eighteenth century Japan was a time of isolation and peace, where education and the arts blossomed. Originally posted before 1749 by an unknown author, the sangaku (mathematical tablet) that became known as the Gion Shrine problem, has…
Over the last decade, Sudoku, a combinatorial number-placement puzzle, has become a favorite pastimes of many all around the world. In this puzzle, the task is to complete a partially filled $9 \times 9$ square with numbers 1 through 9,…
In this letter we will revise the steps followed by A. Einstein when he first wrote on cosmology from the point of view of the general theory of relativity. We will argue that his insightful line of thought leading to the introduction of…
We introduce a very simple solitaire game, named Stanley Solitaire, in honor of Richard Stanley, and prove an explicit closed-form formula for the number of ways of playing it. Alas, the only proof that we know is via a deep theorem of…
Je retracerai l'histoire des conjectures de Weil sur le nombre de solutions d'\'equations polynomiales dans un corps fini et quelques unes des approches qui ont \'et\'e propos\'ees pour les r\'esoudre. The Weil conjectures: origins,…